Problem: Multiply the following complex numbers: $({2+5i}) \cdot ({2-5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2+5i}) \cdot ({2-5i}) = $ $ ({2} \cdot {2}) + ({2} \cdot {-5}i) + ({5}i \cdot {2}) + ({5}i \cdot {-5}i) $ Then simplify the terms: $ (4) + (-10i) + (10i) + (-25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (-10 + 10)i - 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (-10 + 10)i - (-25) $ The result is simplified: $ (4 + 25) + (0i) = 29 $